For a graph $G$, let $cp(G)$ denote the cardinality of a maximum cycle packing (collection of vertex disjoint cycles) and let $cc(G)$ denote the cardinality of a minimum feedback vertex set (set of vertices $X$ so that $G-X$ is acyclic).

In [KLL], the authors mention that there exists a family of nonplanar graphs for which $cc(G) = \Theta( cp(G) \log cp(G) )$, so no such result could hold for general graphs. They also point out that the conjecture is tight for wheels, and they prove it for the special case of outerplanar graphs.

I am Jones. My Taiwanese name is Chuan-Min Lee. This conjecture came up when I was working on it with Ton Kloks and Jiping Liu. I used the name "Jones" instead of my Taiwanese name for ease of communication.